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Summary

Introductory Technical Mathematics, 5th Edition provides current and practical vocational and technical math applications for today's sophisticated trade and technical work environments. Each unit delivers practical math concepts alongside step-by-step examples and problems drawn from various occupations. The plentiful examples and problem sets emphasize on-the-job applications of math.Enhancements to the fifth edition include improved algebra coverage, a new section on basic statistics, new material on conversions from metric to customary systems of measure, and a section that supplements the basics of working with spreadsheets for graphing.

Table of Contents

Preface

xvii

SECTION I Fundamentals of General Mathematics

1

(196)

Unit 1 Whole Numbers

2

(31)

Place Value

2

(1)

Expanding Whole Numbers

3

(1)

Estimating (Approximating)

4

(1)

Addition of Whole Numbers

5

(2)

Subtraction of Whole Numbers

7

(1)

Problem Solving---Word Problem Practical Applications

8

(1)

Adding and Subtracting Whole Numbers in Practical Applications

9

(2)

Multiplication of Whole Numbers

11

(4)

Division of Whole Numbers

15

(3)

Multiplying and Dividing Whole Numbers in Practical Applications

18

(2)

Combined Operations of Whole Numbers

20

(2)

Combined Operations of Whole Numbers in Practical Applications

22

(7)

Unit Exercise and Problem Review

25

(4)

Computing with a Calculator: Whole Numbers

29

(4)

Unit 2 Common Fractions

33

(48)

Definitions

33

(1)

Fractional Parts

34

(1)

A Fraction as an Indicated Division

35

(1)

Equivalent Fractions

35

(1)

Expressing Fractions in Lowest Terms

36

(1)

Expressing Mixed Numbers as Improper Fractions

36

(1)

Expressing Improper Fractions as Mixed Numbers

37

(1)

Division of Whole Numbers: Quotients as Mixed Numbers

38

(1)

Use of Common Fractions in Practical Applications

38

(2)

Addition of Common Fractions

40

(5)

Subtraction of Common Fractions

45

(3)

Adding and Subtracting Common Fractions in Practical Applications

48

(4)

Multiplication of Common Fractions

52

(4)

Multiplying Common Fractions in Practical Applications

56

(3)

Division of Common Fractions

59

(3)

Dividing Common Fractions in Practical Applications

62

(3)

Combined Operations with Common Fractions

65

(2)

Combined Operations of Common Fractions in Practical Applications

67

(7)

Unit Exercise and Problem Review

69

(5)

Computing with a Calculator: Fractions and Mixed Numbers

74

(7)

Unit 3 Decimal Fractions

81

(50)

Meaning of Fractional Parts

82

(1)

Reading Decimal Fractions

82

(1)

Simplified Method of Reading Decimal Fractions

83

(1)

Writing Decimal Fractions

83

(1)

Rounding Decimal Fractions

84

(1)

Expressing Common Fractions as Decimal Fractions

84

(1)

Expressing Decimal Fractions as Common Fractions

85

(1)

Expressing Decimal Fractions in Practical Applications

86

(2)

Adding Decimal Fractions

88

(1)

Subtracting Decimal Fractions

88

(1)

Adding and Subtracting Decimal Fractions in Practical Applications

89

(3)

Multiplying Decimal Fractions

92

(3)

Multiplying Decimal Fractions in Practical Applications

95

(2)

Dividing Decimal Fractions

97

(3)

Dividing Decimal Fractions in Practical Applications

100

(3)

Powers and Roots of Decimal Fractions

103

(3)

Decimal Fraction Powers and Roots in Practical Applications

106

(3)

Table of Decimal Equivalents

109

(3)

Combined Operations of Decimal Fractions

112

(2)

Combined Operations of Decimal Fractions in Practical Applications

114

(11)

Unit Exercise and Problem Review

118

(7)

Computing with a Calculator: Decimals

125

(6)

Unit 4 Ratio and Proportion

131

(15)

Description of Ratios

131

(1)

Order of Terms of Ratios

132

(2)

Description of Proportions

134

(3)

Direct Proportions

137

(2)

Inverse Proportions

139

(7)

Unit Exercise and Problem Review

142

(4)

Unit 5 Percents

146

(18)

Definition of Percent

146

(1)

Expressing Decimal Fractions as Percents

147

(1)

Expressing Common Fractions and Mixed Numbers as Percents

147

(1)

Expressing Percents as Decimal Fractions

148

(1)

Expressing Percents as Common Fractions

149

(1)

Types of Simple Percent Problems

149

(3)

Finding Percentage in Practical Applications

152

(2)

Finding Percent (Rate) in Practical Applications

154

(2)

Finding the Base in Practical Applications

156

(1)

More Complex Percentage Practical Applications

157

(7)

Unit Exercise and Problem Review

160

(4)

Unit 6 Signed Numbers

164

(33)

Meaning of Signed Numbers

164

(2)

The Number Line

166

(1)

Operations Using Signed Numbers

167

(1)

Absolute Value

167

(1)

Addition of Signed Numbers

168

(3)

Subtraction of Signed Numbers

171

(1)

Multiplication of Signed Numbers

172

(2)

Division of Signed Numbers

174

(1)

Powers of Signed Numbers

175

(2)

Roots of Signed Numbers

177

(3)

Combined Operations of Signed Numbers

180

(2)

Scientific Notation

182

(6)

Engineering Notation

188

(9)

Unit Exercise and Problem Review

191

(6)

SECTION II Measurement

197

(96)

Unit 7 Precision, Accuracy, and Tolerance

198

(16)

Exact and Approximate (Measurement) Numbers

198

(1)

Degree of Precision of Measuring Instruments

199

(1)

Common Linear Measuring Instruments

199

(1)

Degree of Precision of a Measurement Number

200

(1)

Degrees of Precision in Adding and Subtracting Measurement Numbers

201

(1)

Significant Digits

202

(1)

Accuracy

203

(1)

Accuracy in Multiplying and Dividing Measurement Numbers

204

(1)

Absolute and Relative Error

204

(1)

Tolerance (Linear)

205

(2)

Unilateral and Bilateral Tolerance with Clearance and Interference Fits

207

(7)

Unit Exercise and Problem Review

209

(5)

Unit 8 Customary Measurement Units

214

(26)

Customary Linear Units

214

(1)

Expressing Equivalent Units of Measure

215

(3)

Arithmetic Operations with Compound Numbers

218

(4)

Customary Linear Measure Practical Applications

222

(3)

Customary Units of Surface Measure (Area)

225

(2)

Customary Area Measure Practical Applications

227

(1)

Customary Units of Volume (Cubic Measure)

228

(1)

Customary Volume Practical Applications

229

(1)

Customary Units of Capacity

230

(1)

Customary Capacity Practical Applications

231

(1)

Customary Units of Weight (Mass)

232

(1)

Customary Weight Practical Applications

233

(1)

Compound Units

233

(2)

Compound Units Practical Applications

235

(5)

Unit Exercise and Problem Review

237

(3)

Unit 9 Metric Measurement Units

240

(28)

Metric Units of Linear Measure

240

(2)

Expressing Equivalent Units within the Metric System

242

(2)

Arithmetic Operations with Metric Lengths

244

(1)

Metric Linear Measure Practical Applications

244

(2)

Metric Units of Surface Measure (Area)

246

(1)

Arithmetic Operations with Metric Area Units

247

(1)

Metric Area Measure Practical Applications

248

(1)

Metric Units of Volume (Cubic Measure)

248

(2)

Arithmetic Operations with Metric Volume Units

250

(1)

Metric Volume Practical Applications

250

(1)

Metric Units of Capacity

251

(1)

Metric Capacity Practical Applications

252

(1)

Metric Units of Weight (Mass)

253

(1)

Metric Weight Practical Applications

254

(1)

Compound Units

254

(2)

Compound Units Practical Applications

256

(1)

Metric Prefixes Applied to Very Large and Very Small Numbers

257

(4)

Conversion Between Metric and Customary Systems

261

(7)

Unit Exercise and Problem Review

264

(4)

Unit 10 Steel Rules and Vernier Calipers

268

(13)

Types of Steel Rules

268

(1)

Reading Fractional Measurements

268

(2)

Measurements that Do Not Fall on Rule Graduations

270

(1)

Reading Decimal-Inch Measurements

271

(1)

Reading Metric Measurements

272

(1)

Vernier Calipers: Types and Description

273

(2)

Reading Measurements on a Customary Vernier Caliper

275

(2)

Reading Measurements on a Metric Vernier Caliper

277

(4)

Unit Exercise and Problem Review

279

(2)

Unit 11 Micrometers

281

(12)

Description of a Customary Outside Micrometer

281

(1)

Reading a Customary Micrometer

282

(1)

The Customary Vernier Micrometer

283

(1)

Reading a Customary Vernier Micrometer

284

(2)

Description of a Metric Micrometer

286

(1)

Reading a Metric Micrometer

286

(1)

The Metric Vernier Micrometer

287

(1)

Reading a Metric Vernier Micrometer

288

(5)

Unit Exercise and Problem Review

290

(3)

SECTION III Fundamentals of Algebra

293

(130)

Unit 12 Introduction to Algebra

294

(11)

Symbolism

294

(1)

Algebraic Expressions

294

(3)

Evaluation of Algebraic Expressions

297

(8)

Unit Exercise and Problem Review

302

(3)

Unit 13 Basic Algebraic Operations

305

(31)

Definitions

305

(1)

Addition

306

(2)

Subtraction

308

(3)

Multiplication

311

(3)

Division

314

(4)

Powers

318

(3)

Roots

321

(3)

Removal of Parentheses

324

(1)

Combined Operations

325

(1)

Basic Structure of the Binary Numeration System

326

(10)

Unit Exercise and Problem Review

330

(6)

Unit 14 Simple Equations

336

(23)

Expression of Equality

336

(1)

Writing Equations from Word Statements

337

(2)

Checking the Equation

339

(2)

Principles of Equality

341

(1)

Solution of Equations by the Subtraction Principle of Equality

341

(3)

Solution of Equations by the Addition Principle of Equality

344

(3)

Solution of Equations by the Division Principle of Equality

347

(2)

Solution of Equations by the Multiplication Principle of Equality

349

(3)

Solution of Equations by the Root Principle of Equality

352

(2)

Solution of Equations by the Power Principle of Equality

354

(5)

Unit Exercise and Problem Review

356

(3)

Unit 15 Complex Equations

359

(14)

Equations Consisting of Combined Operations

359

(4)

Solving for the Unknown in Formulas

363

(1)

Substituting Values Directly in Given Formulas

363

(3)

Rearranging Formulas

366

(7)

Unit Exercise and Problem Review

370

(3)

Unit 16 The Cartesian Coordinate System and Graphs of Linear Equations

373

(12)

Description of the Cartesian (Rectangular) Coordinate System

373

(1)

Graphing a Linear Equation

374

(3)

Slope of a Linear Equation

377

(1)

Slope Intercept Equation of a Straight Line

378

(1)

Point-Slope Equation of a Straight Line

378

(1)

Determining an Equation, Given Two Points

379

(1)

Describing a Straight Line

380

(5)

Unit Exercise and Problem Review

383

(2)

Unit 17 Systems of Equations

385

(18)

Graphical Method of Solving Systems of Equations

385

(2)

Substitution Method of Solving Systems of Equations

387

(1)

Addition or Subtraction Method of Solving Systems of Equations

388

(4)

Types of Systems of Equations

392

(1)

Determinants

393

(1)

Cramer's Rule

394

(1)

Writing and Solving Systems of Equations from Word Statements, Number Problems, and Practical Applications